As usual, my online colleague Ed Staples has provided a succinct solution to this problem. I attach his diagram and result below. You can see that he began by bisecting the chord AB and drawing the perpendicular bisector MC. He calculated the radius of the circle as an exact expression involving square roots, which has an approximate numeric value of 1.5213. This is in agreement with the value I found experimentally when using Geogebra to create the problem. The problem statement is here: https://convexabacus.xyz/index.php/2022/04/11/two-unit-squares-in-a-semicircle/
The problem was shared on LinkedIn where it was solved by Mohamad Saleh. He took a different approach using coordinate geometry and simultaneous equations. I attach his work below in two images.
Diagram (above) and solution (below) by Mohamad Saleh.
